Question: Solve for $x$ and $y$ using substitution. ${6x+3y = 9}$ ${y = -x+4}$
Answer: Since $y$ has already been solved for, substitute $-x+4$ for $y$ in the first equation. ${6x + 3}{(-x+4)}{= 9}$ Simplify and solve for $x$ $6x-3x + 12 = 9$ $3x+12 = 9$ $3x+12{-12} = 9{-12}$ $3x = -3$ $\dfrac{3x}{{3}} = \dfrac{-3}{{3}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -x+4}\thinspace$ to find $y$ ${y = -}{(-1)}{ + 4}$ $y = 1 + 4$ $y = 5$ You can also plug ${x = -1}$ into $\thinspace {6x+3y = 9}\thinspace$ and get the same answer for $y$ : ${6}{(-1)}{ + 3y = 9}$ ${y = 5}$